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His back is up, i.e. he is offended or angry; an expression or idea taken from a cat; that animal, when angry, always raising its back. An allusion also sometimes used to jeer a crooked man; as, So, Sir, I see somebody has offended you, for your back is up.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Backed * BaconNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes
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Francis Grose was independently wealthy, having inherited money from his father, a jeweller. Finding himself overspending, he published a number of books; his Provincial Glossary seems to have been the starting-point for the Vulgar Tongue reproduced here.